%5E4.jpeg "(u^4)^4")
Understanding (u^4)^4
In mathematics, particularly in algebra, we often encounter expressions involving exponents raised to further exponents. One such expression is (u^4)^4. This might seem complex at first glance, but it follows a simple rule: the power of a power rule.
The Power of a Power Rule
The power of a power rule states that when raising a power to another power, we multiply the exponents. This is represented mathematically as:
(a^m)^n = a^(m*n)
Applying this to our expression:
(u^4)^4 = u^(4*4) = u^16
Simplifying the Expression
Therefore, (u^4)^4 simplifies to u^16. This means that u^4 is multiplied by itself four times, resulting in u raised to the power of 16.
Example
Let's consider an example to illustrate this further. Assume u = 2:
(u^4)^4 = (2^4)^4 = (16)^4 = 65536
In this case, (u^4)^4 evaluates to 65536.
Conclusion
Understanding the power of a power rule is essential for simplifying expressions involving exponents. Applying this rule allows us to efficiently simplify expressions like (u^4)^4, resulting in a more concise and manageable form.